QUESTION 33The length of the legs of the right triangle are given as,6 centimeters and 8 centimeters.The length of the hypotenuse can be found using the Pythagoras Theorem.[tex] {h}^{2} = {6}^{2} + {8}^{2} [/tex][tex] {h}^{2} = 36+ 64[/tex][tex] {h}^{2} = 100[/tex][tex]h = \sqrt{100} [/tex][tex]h = 10cm[/tex]Answer: CQUESTION 34The triangle has a hypotenuse of length, 55 inches and a leg of 33 inches.The length of the other leg can be found using the Pythagoras Theorem,[tex] {l}^{2} + {33}^{2} = {55}^{2} [/tex][tex] {l}^{2} = {55}^{2} - {33}^{2} [/tex][tex] {l}^{2} = 1936[/tex][tex]l = \sqrt{1936} [/tex][tex]l = 44cm[/tex]Answer:BQUESTION 35.We want to find the distance between,(2,-1) and (-1,3).Recall the distance formula,[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute the values to get,[tex]d=\sqrt{( - 1-2)^2+(3- - 1)^2}[/tex][tex]d=\sqrt{( - 3)^2+(4)^2}[/tex][tex]d=\sqrt{9+16}[/tex][tex]d=\sqrt{25}[/tex][tex]d = 5[/tex]Answer: 5 units.QUESTION 36We want to find the distance between,(2,2) and (-3,-3).We use the distance formula again,[tex]d=\sqrt{( - 3-2)^2+( - 3- 2)^2}[/tex][tex]d=\sqrt{( - 5)^2+( - 5)^2}[/tex][tex]d=\sqrt{25+25}[/tex][tex]d=\sqrt{50}[/tex][tex]d=5\sqrt{2}[/tex]Answer: D